Modelling Marital Reverse Annuity Contract in a Stochastic Economic Environment

Joanna Dębicka, Stanisław Heilpern, Agnieszka Marciniuk

Statistika, 102(3): 261-281
https://doi.org/10.54694/stat.2022.2

Abstract

In the paper, we present the methodology of calculating the benefit of a marriage reverse annuity using the multiple state model for marriage life insurance. We model the probabilistic structure and cash flows arising from marriage reverse annuity contracts in the case of the joint-life status and the last surviving status assuming that the spouses' future lifetimes are independent. Usually, it is assumed that the interest rate is constant and the same through the years. It is not a realistic assumption. Therefore, this article's purpose is to calculate benefits under the assumption that the interest rate is a stochastic process or a fuzzy number model of the constant interest rate. We conduct a comparative analysis of the amount of benefit (taking into account the different frequency of their payment) for the different models of interest rates.    

Keywords
Stochastic interest rate, fuzzy interest rate, reverse annuity contract, the joint-life status, the last surviving status